Elevating AI Reasoning: The Art of Sampling for Learnability in LLM Training

Reinforcement learning (RL) has been a core component in training large language models (LLMs) to perform tasks that involve reasoning, particularly mathematical problem-solving. A considerable inefficiency occurs during training, including a situation where many questions are always answered or left unsolved. The lack of variability in success rates is to blame for inefficient learning results because questions that do not yield a gradient signal do not allow the model’s performance to be improved. Traditional RL-based fine-tuning strategies are susceptible to expensive computational costs, increased energy usage, and inefficient use of resources. Correcting this is necessary to improve training efficiency and make language models learn from problems that greatly improve their reasoning.

The standard training regimen of large language models (LLMs) uses policy gradient techniques, such as Proximal Policy Optimization (PPO), in which models engage with each query repeatedly and corrections are applied based on signs of success or failure. One of the greatest drawbacks of this approach, however, is that the majority of training examples belong to clusters of extremes—either always correct or always incorrect. When an example is always solved correctly, repeated attempts do not provide further learning information. On the contrary, an impossible query provides no feedback for improvement. As a result, precious computational resources are wasted on useless training scenarios. Different curriculum-learning techniques, such as Unsupervised Environment Design (UED), have attempted to dynamically control training difficulty. These techniques, however, rely on heuristics such as regret-based selection, which are largely insufficient in anticipating optimal problem difficulty and fail to generalize well to reasoning tasks relevant to LLM training.

To address this inefficiency, a novel training policy has been suggested and proposed that focuses on samples with high variance of success rates, thus forcing models to focus on questions not too easy and not too difficult. By identifying and choosing issues where the model performs erratically, the approach concentrates training on scenarios that provide the most informative learning signals. Differing from previous policies that utilized random sampling to train batches, this systematic selection method enhances update efficiency by eliminating problems that do not allow significant improvement. The procedure adapts during training, continuously optimizing question selection to track the fluctuating strength of the model. By targeting instances of moderate difficulty, the approach enables better learning and better generalization to novel tasks.

The structured selection process operates through a multi-step pipeline that begins with the identification of candidate questions at each training iteration. Multiple rollouts are generated to assess the probability of success for each problem, and the variance of these success rates is computed using the function